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The challenging concept of Newtonian mechanics
from philosophical view
Mehdi Jafari Matehkolaee1, Shayan Khorasani2
1
Sama technical and vocational training college, Islamic Azad University,
Sari Branch, Sari, Iran.
2
F Shahid Beheshti High School, Sari, Mazandaran, Iran.
E-mail:[email protected], [email protected]
(Received 24 May 2014, accepted 10 November 2014)
Abstract
We present a brief description from Newton's theory that containing profound points. Afterward we show that based on
the diverse philosophical concepts this theory could be contestable.
Resumen
Se presenta una breve descripción de la teoría de Newton que contiene puntos de reflexión profundos. Después nos
muestran que en base a los diversos conceptos filosóficos esta teoría podría ser discutible
Keywords: Theory of Newton, philosophy.
PACS: 01.40.Fk, 01.65.+g, 01.70.+w
ISSN 1870-9095
We hold that former philosophers such as Aristotle,
Philoponus, and Avicenna, Descartes paved the way for
newtonian mechanics. To emerge our ancestors
contribution and noticeable works into of to-day science
have tried in many literatures. For example Avicenna,
Persian physician and philosopher, was one of the greatest
science philosophers in the history. Today, his contribution
in projectile motion [7] and dynamics [8] is clear. In any
case, Newton's theory is using as a powerful theory whether
touched of his ancestors or considerable works that he did
in his contemporary. We know that even the principle of
least action that we can conclude Newton's second law from
it, is a strong confirmed for Newton's theory. However,
there are some debates that with respect to them, this theory
can be contestable.
I. INTRODUCCIÓN
Now, it is more than 300 years that newtonian mechanics is
accepted as one of the fundamental branches in physics
science. Many phenomena in macroscopic dimension can
be explained indisputably. Even in relativity, newtonian
time conception is confirmed and the only thing that
changes is manner of measurement. Also in quantum
mechanics many structures and mathematical patterns has
extracted of Newtonian mechanics. If we don’t consider
relativity and quantum mechanics then, in the same
macroscopic world, there are different reasons that indicate
newtonian mechanics is containing of arguments so that can
be contestable.
Physicists at the end of 19th century reached the
consensus that the relation F=ma was just a definition,
because the only quantity that can be measured
unambiguously is the acceleration [1, 2].
Some researchers have performed in the attention to
modify Newton’s second law and experimentally test for it
[3, 4, 5, 6]. First we should point that, although structural
engineering science and relief progresses of it is based on
the newtonian dynamics but many before 17th century have
constructed magnificent buildings that complexity and
fragility have done in them are witness violence of builders
on the construction science. In addition to this, what we are
reading in kinematics and dynamics was evaluating as
natural science and was proving in philosophical debates
with more qualitative cases, which were forgotten because
of emergence of some people such as Galileo and Newton
so that substituted by quantitative laws.
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II. NEWTON'S THEORY IN A GLANCE
Before Newton, Avicenna has presented an important
philosophical conception which is the dualism between
subject and object. Also, Descartes tried to algebraic
geometry and definition coordinates and they prepared
conditions for Newton's theory [9]. Since both of these
cases (dualism and algebraic geometry) do use in
newtonian mechanics. For example in classical mechanics
we consider physical parameters belong to body as
objective qualities. There is one question once more: do
object’s geometrical dimensions have impressive
contribution in this view? Avicenna held that object’s
geometrical dimensions influence on the celerity and
sluggishness, but Jean Buridan didn't accept that.
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Mehdi Jafari Matehkolaee, Shayan Khorasani
In any case, we conclude of differential form of
Newton's second law that force is an instantly-pointy
quantity. When we set F on the system contain of n bodies
so that all of them have the same acceleration such as
following Figure 1, then we consider them as a point
inattentive to their geometrical dimensions.
F
m1
m2
In Newtonian mechanics position and velocity are the
two dynamical variables so that connect each other with
time.
Position as function of time gets the equation of motion.
The reasons of motion of physical objects are described
by the metaphysical conception of force, directly.
mn
Force:
metaphysical
conception
Time
Position
FIGURE 1. In this figure see inumerable objects at the
firictionless surface.
Pure parameter
Physical
object
Since in Figure 1 the horizontal surface is frictionless, then
we can write:
.
Analysis on physical system
FIGURE 2. A general schematic of analysis object's motion.
The left part of the diagram shows dynamical analysis, and
the other part represents kinematical analysis, so that both
of them are consistent with each other.
III. NEWTON'S THEORY IN CHALLENGE
The most important supporter of Newton's principle is
experiment and observation. If F doesn’t insert to
in
Figure 1, we have to assume that there is no force between
objects. In fact in this situation, although the objects have
contact with each other but they don’t have any interaction.
Indeed, generally, we can know the interaction between
two objects when, we enter a force to one of them. In
matter fact, to know the situation of a distinguished
physical system, our interference is necessary for
measuring in system.
Sometimes, necessity of our interference will be so
further up, especially in cases that we have to use the
concept of virtual forces. For example, consider a person in
an elevator and there is an object at rest on floor of the
elevator.
If the elevator doesn’t move, the person will attribute
the following relation:
(2)
Perhaps in the reductionism analysis full definition from
Newton's second law is as following:
The ratio of result of forces that set on the system
directly and from out of system, than mass of the system is
equal to its acceleration.
In this definition system is the set of the objects so that
all of them have the same acceleration.
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Dynamical variable
(1)
Relation 1 shows that the set of bodies (
)
are similar to a point (center of mass) so that in moment of
t, F set on it.
Obviously, dimension of objects has no contribution in
relation 1. Now, let us to investigate reductionism in this
argument. We know newtonian mechanics is corresponding
with reductionism philosophical view. Based on this view,
analysis behavior of parts of a system is equivalent to total
of system and the total have nothing more than set of parts.
If we want to write an equation for objects in Figure 1
according to reductionism, then at first we should state that
F only set on
.
Next, by writing Newton's second law in horizontal
direction for each one of them and combine these
equations, led to Equation 1.
The analysis being in textbooks, free-body diagram is
compatible with reductionism. When can we write a general
equation directly similar relation 1 for a system formed
with many bodies?
The answer is clear. This is true when all of the bodies
have the same acceleration. But if we return to differential
form of Newton's second law, we will found an important
point. Although, force set in the point of space and instant
of time, but force is a curvature in the space-time diagram.
The amount of this curvature gets the following relation
[10].
.
velocity
.
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The challenging concept of newtonian mechanics from philosophical view
correct when the force doesn’t have a metaphysical
concept.
For an instance in free fall we have:
That N is the force which the floor of the elevator inserts to
object and mg is the weight of it. Now imagine that the
elevator has ascending motion with constant acceleration a.
The person see object at rest again but for that reason
Newton’s theory has to hold then he must consider
following equation:
.
(9)
So:
.
(4)
.
Where
is virtual force so that is downward. However,
the main question is remained that what amounts can
interference the awareness of person? Which criterion is
there for that?
In Newton’s second law, external forces are the causes
of motion. When we survey the changing of a physical
system by external causes around it, the main problem is
the force itself. That is to say the force doesn’t have a
diagnostic metaphysical concept. Indeed, the forces are
understood by Newton’s second law principle. In many
dynamical problems, acceleration of a physical system
ascertains the incoming forces (for an instance in machines
of Atwood, first we calculate the acceleration of objects
then we calculate the tension of string).
We know that force can be a function of position,
velocity and time
.
How do we know a force with metaphysical concept,
amount of
is equal to zero? We need for finding the
solution of an nth differential equation, n constants that are
called integration constant and (n-1) times derivative at the
initial point. With respect to newtonian mechanics, initial
position
and its first derivative
are not determined
and they can change, but other derivatives (second
derivative or initial acceleration, third derivative are
distinguished. The first comment for proposed equation is
state
.
.
Indeed by one time integration from Newton’s equation we
have:
(5)
(11)
Suppose we want to propose an equation like Newton did.
But this time, the equation is more general:
.
So that
(10)
The first objection to this equation is that as we said, we
can change
and
at pleasure in special conditions and
its follower, momentum ( ) isn’t able to appoint with an
equation like relation (11).
(6)
can be like the following equation:
.
.
(7)
And the second objection is that
had to show the effect
of the object’s perimeter environment but, it’s obvious that
looks unintelligible in the conditions like encountering.
We know in Newtonian mechanics, position of a system
could not have leap as a function of time. But velocity can
have leap in fast and sudden encountering. For example,
consider a motionless object which in instant of zero takes
by a sudden encountering and thereafter continues with
without any obstacle.
It’s worthy of attention that in state n=2 and considering
like Newton’s force, the proposed equation
will be Newton’s equation. Relation 6 is important because
force can be a function of acceleration, jerk and…while that
is function of position, velocity and time. Here there is a
problem similar to 19th century physicists yet, because mass
parameter plays the same contribution. Now without this
matter we will try to distinguish. What that substitute in
F(n).
But a pre-proposition is necessary. This pre-proposition
holds the theory of Newton. We derivative n-2 times of
forces that is correct in Newton’s relation, for
.
.
(13)
It means that the object doesn’t fell anything from the
stroke till before encountering and thereafter it receives
effect from environment foreverǃ As we know
, is
object’s linear momentum. It means that it’s an attribute for
it, not something which tells us the environment’s effect.
About zeroth state should say that
(8)
Note that by each time integration the constant value adds
to equation that we can face it by a method, which cause the
last answer be Newton’s equation. Of course this matter is
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.
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Mehdi Jafari Matehkolaee, Shayan Khorasani
[5] Yu, A., Ignatiev, is violation of Newton’s second law
possible?, Phys. Rev. Lett. 98, 101101 (2007).
[6] Hacyan, S. What does it mean to modify or test
Newton’ssecond law? Am. J. Phys. 77, 607-609 (2009).
[7] Sayili, A., Ibn Sina and Buridan on the motion of the
projectile, Annals of the New York academy of sciences
500, 477-482 (1987).
[8] Feliz-Teixeria, J. M., Deducing Kepler and Newton
from Avicenna, Huygens and Descartes, Reviewed in:
http://www.fe.up.pt/~feliz, visited on 15 February 2014.
[9] Wheeler, D., Calculations with whole vectors: A really
easy alternative to components, Phys. Educ. 36, 406-409
(2001)
[10] Fowles, G. R. and Cassiday, G. L., Analytical
Mechanics, 6th Ed. (Harcourt Brace College Publishers,
USA, 1999).
[11] Feynman, R. P., Lectures on Physics, Vol. 1,
(Addison-Wesley,
Redwood
City:
USA,
1963).
It means that we can know the position of object, when we
know where is it!!
REFERENCES
[1] Mach, E., The science of mechanics, (Open Court
Publishing Company, La Salle: USA, 1989).
[2] Jammer, M., Concepts of force, (Harvard University
Press: Cambridge, Massachusetts, 1957).
[3] Milgrom, M., A modification of the Newtonian
dynamics as a possible alternative to hidden math
hypothesis, Astrophys. J. 270, 365-370 (1983).
[4] Abramovici, A. and Z. Vager, Test for Newton’s second
law at small accelerations, Phys. Rev. D34, 3240-3241
(1986).
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